Using Fuzzy Sets To Define the Information’s Quantity

Information is considered as a change of a fuzzy set expressing a state. In this case, a mange of state is equivalent to a change in the grade of membership ()A xµ ∆ of an element x belonging to a fuzzy set A. The quantity of information can be computed using certain functions, called informational functions. Four axioms are presented, which must be satisfied by any informational function. In the case of information accumulation, they will organize themselves in a pattern. The intensity of the relation between two elements x∈A and y∈A at time 0t is measured by a grade of membership. In this case, the information gain is expressed by the change of the grade of membership ()A xµ ∆ . Some examples are given from the field of figures of speech used by writers. In the case of metaphor, the concept of author-reader communication is defined as the possibility an educated reader has of "guessing" the author's intentions. In the algorithm used by the reader to decipher the message, the grade of membership to the author's message should increase at every step, ideally converging to one. JEL Classification: C02,C23,C4